
where \(\mathbf {R}=\sum _{k=1}^{K}2\omega _{k}\eta _{k,2}\mathbf {h}_{k}\mathbf {h}_{k}^{H}\) ,
\(\mathbf {p}_{k}=\omega _{k}\frac{\eta _{1,k}\alpha _{k}}{|\alpha _{k}|}\mathbf {h}_{k}\) ,
and the optimal dual variable \(\lambda ^{\star }>0\)  satisfies \(\sum _{k=1}^{K}\Vert (\mathbf {R}+2\lambda ^{\star }\mathbf {I})^{-1}\mathbf {p}_{k}\Vert _{2}^{2}=P_{\mathsf {max}}\) 
and can be readily found via one-dimensional line search methods [1]}
to meetA further majorization can be applied to the objective in (REF )
for a closed-form solution without line search, which is not detailed
due to space limitation.
